Isomorphism identification of kinematic chain topology embryonic graphs

Isomorphism identification of topology embryonic graphs is a key link in plane parallel mechanism synthesis methods based on embryonic graph. Aiming at kinematic chains topology embryonic graph without binary links, the problem of isomorphism identification among them is solved. Topology embryonic graph has unique feature against topology graph. Because there aren't binary vertices in limbs of topology embryonic graph, relation among vertices are largely relative position among them. According to the feature of topology embryonic graph, the matrix of path number among any vertices of topology embryonic graph is set up from the classical theory of adjacency matrix about graph. The items of the path number matrix are arranged into path array according to certain rule. The isomorphic condition for topology embryonic graphs is demonstrated. Topology embryonic graphs are identified if they are isomorphic by second order path array when degree sequence and first order path array are same. Examples are given to illustrate identification procedure and specific application. Solution to the problem of isomorphism identification of topology embryonic graph not only lays the foundation for type synthesis based on embryonic graph, but also there is universal significance for isomorphism identification of some kinematic chain topology graphs. © 2012 Journal of Mechanical Engineering.